ALTANA Mandrel Set - Manual (Page 6)

5
Theory
When a test panel of known uniform thickness is
bent closely around a mandrel of known diameter,
the THEORETICAL change in length of the faces
of the panel may be calculated. After bending,
the outer curved surface will have been stretched
a certain amount, the inner surface compressed
an equal amount, and a plane midway between
these faces will have remained the same length.
Based on this theory, the percent elongation of the
outer (usually coated) surface is simply 100 t/(D+t)
where „t‘‘ is the thickness of the panel and „D“ is
the diameter of the cylindrical mandrel. For a 1/32“
panel bent over a 1/8“ mandrel, the percent
elongation would be 100 x 1/32 (4/32 + 1/32) =
100 x 1/5 = 20%.
The ACTUAL change in length of the surfaces
will vary from the theoretical changes by a small
difference in percentage that is a factor of the ma-
terial being used, the panel thickness and mandrel
diameter. This discrepancy between the calculated
and true percent elongations is seen in the fol-
lowing table describing a cold-rolled steel panel
1/32“ thick.
Diameter of Mandrel 1-1/2” 1” 3/4” 1/2” 1/4” 1/8”
Theoretical % Elongation 2.0 3.0 4.0 5.9 11.1 20.0
Actual % Elongation - 3.3 - 6.7 13.8 28.0
The discrepancy occurs because the plane at
which no stress or compression is experienced is
not found exactly halfway between the two faces
of the panel. In the above example, the level of
no change in length is encountered closer to the
bottom surface than the top and gets closer to
Theory